Tagged Questions

This covers all transformations of functions by integrals, including but not limited to the Radon, X-Ray, Hilbert, Mellin transforms. Use (wavelet-transform), (laplace-transform) for those respective transforms, and use (fourier-analysis) for questions about the Fourier and Fourier-sine/cosine ...

During my research i'm dealing with a stochastic partial differential equation.
The random term appearing in my equation is a tensorial random variable:
$\boldsymbol{\sigma}(\boldsymbol{x},t)$
Which ...

I've recently been studying wavelet analysis with a view to differentiating certain areas of texture images where the texture differs from the background pattern (which is quite random); for example a ...

Given a function $f:\mathbb{R}\rightarrow\mathbb{R}$ we take the generalised Fourier transform $\hat{f}(w)=\int_{-\infty}^{+\infty}e^{iwx}f(x)dx$ where $w\in \mathbb{C}$.
Now assume, this transform ...

Wolfram Alpha gave me the answer to this, but unfortunately Wolfram Alpha doesn't show its work, I can't find a proof anywhere else, and my feeble attempts to show it myself went nowhere. How can it ...

Fix a certain $x \in \mathbb{R}^{n}.$ Let us denote by $\omega_{n}$ the surface area of the unit sphere. Let $g(\pi)$ be a function defined in the set of hyperplanes, $\mathcal{P}$. Such a function ...

I am using the sctoolbox for Matlab from T. Driscoll to transform the upper complex halfplane onto an area given by the three points x1=-1 and x2=1i. The thrid point is at infinity. This works fine ...

The integral $$\int_0^{\infty} e^u \ K_{i t}(u) du$$ is the adjoint Kontorovich-Lebedev transform of the increasing exponential function, but unfortunately this integral is divergent because $$e^u \ ...

There are for example several canonical spaces to define the Fourier transform (i.e. Schwartz's space). Is there also a particularly suitable space to define the Laplace transform, so that the Laplace ...

As mentioned in another post, as a consequence of Mittag-Leffler's theorem combined with the Weierstrass factorization theorem, after reducing to the common denominator, any meromorphic function can ...

Suppose we have the integral operator $T$ defined by
$$Tf(y) = \int_{-\infty}^{\infty} e^{-\frac{x^2}{2}}f(xy)\,dx,$$
where $f$ is assumed to be continuous and of polynomial growth at most (just to ...